NEW HAVEN, Conn. — Supreme Court Justice Sonia Sotomayor, who grew up poor in New York City, described Monday how she navigated new worlds of Ivy League universities and the nation’s highest court.

Sotomayor told students at Yale University that she has a competitive drive to improve herself and isn’t afraid to ask questions.

Sotomayor, the first Hispanic on the U.S. Supreme Court, said she didn’t even know what an Ivy League college was when a friend suggested she apply. She wound up attending Princeton and Yale Law School.

On the Supreme Court since 2009, Sotomayor said it was tough at first as justices made references that went over her head. She said joining the high court amounted to joining an ongoing conversation among justices who had served for years.

“I figure I may not be the smartest judge on the court but I’m going to be a competent justice,” she said. “I’m going to try to be the best I can and each year I think my opinions have been getting better. And I’m working at finding my voice a little bit.”

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Sotomayor was asked at a talk at Yale Law School later in the day about her use of the term “undocumented immigrants” rather than the traditional illegal alien. Sotomayor characterized the issue as a regulatory problem and said labeling immigrants criminals seemed insulting to her.

“I think people then paint those individuals as something less than worthy human beings and it changes the conversation,” Sotomayor said.

Sotomayor was interviewed by Judith Resnik, a Yale law professor, in front of a large audience and later by Linda Greenhouse, a journalist-in residence and lecturer at the law school. The earlier questions focused on her memoir, “My Beloved World,” published last year.

The 59-year-old justice said she quickly left an interview to attend Harvard, feeling she didn’t belong. She said Yale students in the 1970s were talking about revolutions in Cuba and other countries while she had attended a Catholic high school where the monsignor supported the Vietnam War.

“This is too progressive for me,” she said of Yale, sparking laughter. “Yeah, strange, right?”

Sotomayor learned how to adapt, finding strength in her culture and getting a broader understanding of the world. She compared it to a bird that flies to different places.

“Learn what the world has to offer and come back to the nest when you need a little bit of comfort,” Sotomayor said.

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She admitted that she sometimes finds herself stuck between two worlds, one in which her colleagues talk of operas and another in which she sees a cockroach in an apartment in her old Bronx neighborhood and flees.

“Sometimes I do feel I’m not part of either world completely,” she said. “My life has changed so much that going back I don’t feel I’m completely part of the conversation.”

But she said she’s found overlaps in both worlds that keep her connected, such as common emotions of love and caring.

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